75264 has 60 divisors (see below), whose sum is σ = 233244. Its totient is φ = 21504.

The previous prime is 75253. The next prime is 75269. The reversal of 75264 is 46257.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

Its product of digits (1680) is a multiple of the sum of its prime divisors (12).

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 75264.

It is not an unprimeable number, because it can be changed into a prime (75269) by changing a digit.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 10749 + ... + 10755.

2⁷⁵²⁶⁴ is an apocalyptic number.

75264 is the 147-th nonagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75264, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (116622).

75264 is an abundant number, since it is smaller than the sum of its proper divisors (157980).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

75264 is an equidigital number, since it uses as much as digits as its factorization.

75264 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 35 (or 12 counting only the distinct ones).

The product of its digits is 1680, while the sum is 24.

The square root of 75264 is about 274.3428511917. The cubic root of 75264 is about 42.2210567032.

Multiplying 75264 by its sum of digits (24), we get a square (1806336 = 1344²).

75264 divided by its sum of digits (24) gives a square (3136 = 56²).

The spelling of 75264 in words is "seventy-five thousand, two hundred sixty-four".